This proposal requests support to continue the training program in Modeling of Cognitive at Indiana University. The program, now finishing its tenth year, has provided support for two postdoctoral fellows, and two predoctoral trainees per year. The program has twelve core faculty, ten of whom are in the Psychology Department, and are internationally recognized for their expertise in the modeling of cognition; they have contributed some of the major models of cognition in the field, also many important methodological innovations and techniques. There are in addition 21 affiliated faculty within the Cognitive Science Program at Indiana who model cognition in their research, and provide auxiliary support for the program. Mathematical and computer simulation models of cognitive processes are increasing in importance year by year as the field begins to tackle the true complexity of cognition, and apply the results to problems of important national priority (in education, health, and problem solving in government and business). The unpredictability of outcomes from highly interactive systems makes it impossible to rely upon intuitive predictions, and makes modeling imperative. Our training program provides a wide range of experience in many techniques, including formal mathematical models, stochastic processes, non-linear dynamical systems, and neural net modeling, also provides examples of applications in many areas of cognition, including memory and learning, psycholinguistics, visual and auditory processing, speech production and perception, skill acquisition, categorization and conceptualization, decision making, problem solving, attention, and automatization. The four pre-doctoral trainees will be selected from applicants for graduate study to the Psychology Department, and take a five year program resulting in a joint Ph.D. in Psychology and Cognitive Science, and a Certificate in Modeling in Cognitive Science. Their program will emphasize laboratory research and modeling of the empirical results, with experience in the labs of at least two of the core faculty. The four post-doctoral trainees will visit for two years each, taking modeling courses and carrying out research involving modeling in the laboratories of one or more of the core faculty. Training of both groups will be given in a wide variety of mathematical and computer simulation modeling techniques, the application of models to data (including requisite techniques of data analysis), the testing and comparison of models, and the exploration of models and their implications. They will participate in and present their research in weekly seminars, attend colloquia, submit their research to professional journals, and present the research at meetings.